Post on 29-Oct-2019
NeutrinoMassOrdering:HintsandChallenges
ßRenéMagri+e,VoiceofSpace(1931)
EligioLisi(INFN,Bari,Italy)
SolvayνWorkshop,Brussels,2017
OUTLINE:• Prologue:3νknownsandunknowns• Global3ν oscillaFonanalysisandmassordering• CombinaFonwithnonoscillaFonconstraints• Futurechallenges• Epilogue
Mainlybasedon:
F.Capozzi,E.DiValenFno,E.Lisi,A.Marrone,A.Melchiorri,A.Palazzo,“Globalconstraintsonabsoluteneutrinomassesandtheirordering”
arXiv:1703.04471[PRD95,096014(2017)]
Forindependentanalyses,seealsoEsteban+1611.01514;deSalas+1708.01186
2
U↵i =
2
41 0 00 c23 s230 �s23 c23
3
5
2
4c13 0 s13e�i�
0 1 0�s13ei� 0 c13
3
5
2
4c12 s12 0�s12 c12 00 0 1
3
5
2
41 0 00 ei↵/2 00 0 ei�/2
3
5
Mixings and phases: CKMà PMNS (Pontecorvo-Maki-Nakagawa-Sakata)
Extra CPV phases [if Majorana]
not tested in oscillat.
Mass [squared] spectrum (E ~ p + m2/2E + “interaction energy” )
1 2
1 2
δm2
δm2
Δm2
Δm2
“Normal” Ordering NO
“Inverted” Ordering IO
+ interactions in matter à effective terms ~ GF . E . density
+ absolute mass scale (not tested in oscillations)
2-3 rotation 1-3 rotation + CPV “Dirac” phase
1-2 rotation
3
3
Prologue:3νparadigm-parameters 3
ν flavor oscillation experiments: α à β in vacuum and matter
a
b
c
d
e
f
g
eàe (KamLAND), θ12 )
eàe (Solar) θ12 )
µàµ (Atmospheric) ( Δm2 , θ23 )
µàµ (LBL Accel) Δm2 , θ23 )
eàe (SBL Reac.) θ
µàe (LBL Accel) θ
µàτ (OPERA, SK)θ Data from various types of neutrino experiments: (a) solar, (b) long-baseline reactor, (c) atmospheric, (d) long-baseline accelerator, (e) short-baseline reactor, (f,g) long baseline accelerator (and, in part, atmospheric). (a) KamLAND [plot]; (b) Borexino [plot], Homestake, Super-K, SAGE, GALLEX/GNO, SNO; (c) Super-K atmosph. [plot], DeepCore, MACRO, MINOS etc.; (d) T2K (plot), MINOS, K2K; (e) Daya Bay [plot], RENO, Double Chooz; (f) T2K [plot], MINOS, NOvA; (g) OPERA [plot], Super-K atmospheric.
4
Leading sensitivities to 3ν oscillation parameters:
a
b
c
d f
g
eàe ( δm2 , θ12 )
eàe ( δm2 , θ12 )
µàµ ( Δm2 , θ23 )
µàµ ( Δm2 , θ23 )
eàe ( Δm2 , θ13 )
µàe ( Δm2 , θ13 , θ23 )
µàτ ( Δm2 , θ23 ) Data from various types of neutrino experiments: (a) solar, (b) long-baseline reactor, (c) atmospheric, (d) long-baseline accelerator, (e) short-baseline reactor, (f,g) long baseline accelerator (and, in part, atmospheric). (a) KamLAND [plot]; (b) Borexino [plot], Homestake, Super-K, SAGE, GALLEX/GNO, SNO; (c) Super-K atmosph. [plot], DeepCore, MACRO, MINOS etc.; (d) T2K (plot), MINOS, K2K; (e) Daya Bay [plot], RENO, Double Chooz; (f) T2K [plot], MINOS, NOvA; (g) OPERA [plot], Super-K atmospheric.
5
“Broad-brush” 3ν picture (with 1-digit accuracy)
+Δm2
δm2 m2ν
ν2 ν1
ν3
ν3 -Δm2
e µ τ
δm2 ~ 7 x 10-5 eV2
Δm2 ~ 2 x 10-3 eV2
sin2θ12 ~ 0.3 sin2θ23 ~ 0.5 sin2θ13 ~ 0.02
δ = Dirac CPV phase
sign(Δm2) = ordering
“octant” of θ23 absolute mass scale Dirac/Majorana nature
Knowns: Unknowns:
Normal Ordering (NO) Inverted Ordering (IO)
6
Hi-res and larger picture à Global analysis of ν oscill. data
χ2 metric adopted. Parameters not shown are marginalized away:
C.L.’s refer to Nσ = √ Δχ2 = 1, 2, 3, ...
Analysis includes increasingly rich oscillation data sets:
LBL Acc + Solar + KL LBL Acc + Solar + KL + SBL Reactor LBL Acc + Solar + KL + SBL Reactor + Atmosph.
Global fit results taken from 1703.04471 . Note: KL=KamLAND.
7
6.5 7 7.5 8 8.50
1
2
3
4
2 2.2 2.4 2.6 2.80
1
2
3
4
0 0.5 1 1.5 20
1
2
3
4
0.25 0.3 0.350
1
2
3
4
0.01 0.015 0.02 0.025 0.030
1
2
3
4
0.3 0.4 0.5 0.6 0.70
1
2
3
4
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND + SBL Reactors + Atmos
NOIO
Current 1σ errors (1/6 of ±3σ range):
Note: Δm2 = (Δm2
31 + Δm232)/2
Five known oscillation parameters:
δm2 2.3 % Δm2 1.6 % sin2θ12 5.8 % sin2θ13 4.0 % sin2θ23 ~ 9 %
all<10%...2-3digitsneeded
à Precision Era!
[but: PMNS still very far from CKM accuracy]
à novel expt+theo challenges (fluxes, cross sections, ...) in nuclear physics
6.5 7 7.5 8 8.50
1
2
3
4
2 2.2 2.4 2.6 2.80
1
2
3
4
0 0.5 1 1.5 20
1
2
3
4
0.25 0.3 0.350
1
2
3
4
0.01 0.015 0.02 0.025 0.030
1
2
3
4
0.3 0.4 0.5 0.6 0.70
1
2
3
4
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND + SBL Reactors + Atmos
NOIO
8
6.5 7 7.5 8 8.50
1
2
3
4
2 2.2 2.4 2.6 2.80
1
2
3
4
0 0.5 1 1.5 20
1
2
3
4
0.25 0.3 0.350
1
2
3
4
0.01 0.015 0.02 0.025 0.030
1
2
3
4
0.3 0.4 0.5 0.6 0.70
1
2
3
4
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND + SBL Reactors + Atmos
NOIO
θ23 octant
δCP
Three unknown oscillation parameters
NO or IO
9
6.5 7 7.5 8 8.50
1
2
3
4
2 2.2 2.4 2.6 2.80
1
2
3
4
0 0.5 1 1.5 20
1
2
3
4
0.25 0.3 0.350
1
2
3
4
0.01 0.015 0.02 0.025 0.030
1
2
3
4
0.3 0.4 0.5 0.6 0.70
1
2
3
4
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.015 0.02 0.025 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND
NHIH
LBL+Sol+KL
θ23
Δχ2 (IO-NO)
octant
+1.1
12θ2sin0.25 0.30 0.35
0
1
2
3
4
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03 0.04
2 eV -5/102mδ6.5 7.0 7.5 8.0 8.50
1
2
3
4
2 eV -3/102m∆2.0 2.2 2.4 2.6 2.8
π/δ0.0 0.5 1.0 1.5 2.0
LBL Acc + Solar + KL + SBL Reactors
σNσN
NHIH
More on unknown oscillation parameters:
6.5 7 7.5 8 8.50
1
2
3
4
2 2.2 2.4 2.6 2.80
1
2
3
4
0 0.5 1 1.5 20
1
2
3
4
0.25 0.3 0.350
1
2
3
4
0.01 0.015 0.02 0.025 0.030
1
2
3
4
0.3 0.4 0.5 0.6 0.70
1
2
3
4
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.015 0.02 0.025 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND
NHIH
12θ2sin0.25 0.30 0.35
0
1
2
3
4
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03 0.04
2 eV -5/102mδ6.5 7.0 7.5 8.0 8.50
1
2
3
4
2 eV -3/102m∆2.0 2.2 2.4 2.6 2.8
π/δ0.0 0.5 1.0 1.5 2.0
LBL Acc + Solar + KL + SBL Reactors
σNσN
NHIH
δCP
6.5 7 7.5 8 8.50
1
2
3
4
2 2.2 2.4 2.6 2.80
1
2
3
4
0 0.5 1 1.5 20
1
2
3
4
0.25 0.3 0.350
1
2
3
4
0.01 0.015 0.02 0.025 0.030
1
2
3
4
0.3 0.4 0.5 0.6 0.70
1
2
3
4
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND + SBL Reactors + Atmos
NOIO
10
6.5 7 7.5 8 8.50
1
2
3
4
2 2.2 2.4 2.6 2.80
1
2
3
4
0 0.5 1 1.5 20
1
2
3
4
0.25 0.3 0.350
1
2
3
4
0.01 0.015 0.02 0.025 0.030
1
2
3
4
0.3 0.4 0.5 0.6 0.70
1
2
3
4
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND + SBL Reactors
NHIH
6.5 7 7.5 8 8.50
1
2
3
4
2 2.2 2.4 2.6 2.80
1
2
3
4
0 0.5 1 1.5 20
1
2
3
4
0.25 0.3 0.350
1
2
3
4
0.01 0.015 0.02 0.025 0.030
1
2
3
4
0.3 0.4 0.5 0.6 0.70
1
2
3
4
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.015 0.02 0.025 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND
NHIH
LBL+Sol+KL +SBL Reac
θ23
Δχ2 (IO-NO)
octant
+1.1 +1.1
12θ2sin0.25 0.30 0.35
0
1
2
3
4
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03 0.04
2 eV -5/102mδ6.5 7.0 7.5 8.0 8.50
1
2
3
4
2 eV -3/102m∆2.0 2.2 2.4 2.6 2.8
π/δ0.0 0.5 1.0 1.5 2.0
LBL Acc + Solar + KL + SBL Reactors
σNσN
NHIH
6.5 7 7.5 8 8.50
1
2
3
4
2 2.2 2.4 2.6 2.80
1
2
3
4
0 0.5 1 1.5 20
1
2
3
4
0.25 0.3 0.350
1
2
3
4
0.01 0.015 0.02 0.025 0.030
1
2
3
4
0.3 0.4 0.5 0.6 0.70
1
2
3
4
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.015 0.02 0.025 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND
NHIH
12θ2sin0.25 0.30 0.35
0
1
2
3
4
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03 0.04
2 eV -5/102mδ6.5 7.0 7.5 8.0 8.50
1
2
3
4
2 eV -3/102m∆2.0 2.2 2.4 2.6 2.8
π/δ0.0 0.5 1.0 1.5 2.0
LBL Acc + Solar + KL + SBL Reactors
σNσN
NHIH
δCP
6.5 7 7.5 8 8.50
1
2
3
4
2 2.2 2.4 2.6 2.80
1
2
3
4
0 0.5 1 1.5 20
1
2
3
4
0.25 0.3 0.350
1
2
3
4
0.01 0.015 0.02 0.025 0.030
1
2
3
4
0.3 0.4 0.5 0.6 0.70
1
2
3
4
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND + SBL Reactors
NHIH
6.5 7 7.5 8 8.50
1
2
3
4
2 2.2 2.4 2.6 2.80
1
2
3
4
0 0.5 1 1.5 20
1
2
3
4
0.25 0.3 0.350
1
2
3
4
0.01 0.015 0.02 0.025 0.030
1
2
3
4
0.3 0.4 0.5 0.6 0.70
1
2
3
4
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND + SBL Reactors + Atmos
NOIO
6.5 7 7.5 8 8.50
1
2
3
4
2 2.2 2.4 2.6 2.80
1
2
3
4
0 0.5 1 1.5 20
1
2
3
4
0.25 0.3 0.350
1
2
3
4
0.01 0.015 0.02 0.025 0.030
1
2
3
4
0.3 0.4 0.5 0.6 0.70
1
2
3
4
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND + SBL Reactors + Atmos
NOIO
More on unknown oscillation parameters: 11
6.5 7 7.5 8 8.50
1
2
3
4
2 2.2 2.4 2.6 2.80
1
2
3
4
0 0.5 1 1.5 20
1
2
3
4
0.25 0.3 0.350
1
2
3
4
0.01 0.015 0.02 0.025 0.030
1
2
3
4
0.3 0.4 0.5 0.6 0.70
1
2
3
4
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND + SBL Reactors
NHIH
6.5 7 7.5 8 8.50
1
2
3
4
2 2.2 2.4 2.6 2.80
1
2
3
4
0 0.5 1 1.5 20
1
2
3
4
0.25 0.3 0.350
1
2
3
4
0.01 0.015 0.02 0.025 0.030
1
2
3
4
0.3 0.4 0.5 0.6 0.70
1
2
3
4
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.015 0.02 0.025 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND
NHIH
LBL+Sol+KL +SBL Reac +Atmos
θ23
Δχ2 (IO-NO)
octant
+1.1 +1.1 +3.6
Max-mixing disfavored; octant flips with NO/IO
Intriguing! NO favored
12θ2sin0.25 0.30 0.35
0
1
2
3
4
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03 0.04
2 eV -5/102mδ6.5 7.0 7.5 8.0 8.50
1
2
3
4
2 eV -3/102m∆2.0 2.2 2.4 2.6 2.8
π/δ0.0 0.5 1.0 1.5 2.0
LBL Acc + Solar + KL + SBL Reactors
σNσN
NHIH
6.5 7 7.5 8 8.50
1
2
3
4
2 2.2 2.4 2.6 2.80
1
2
3
4
0 0.5 1 1.5 20
1
2
3
4
0.25 0.3 0.350
1
2
3
4
0.01 0.015 0.02 0.025 0.030
1
2
3
4
0.3 0.4 0.5 0.6 0.70
1
2
3
4
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND + SBL Reactors + Atmos
NOIO
6.5 7 7.5 8 8.50
1
2
3
4
2 2.2 2.4 2.6 2.80
1
2
3
4
0 0.5 1 1.5 20
1
2
3
4
0.25 0.3 0.350
1
2
3
4
0.01 0.015 0.02 0.025 0.030
1
2
3
4
0.3 0.4 0.5 0.6 0.70
1
2
3
4
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.015 0.02 0.025 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND
NHIH
12θ2sin0.25 0.30 0.35
0
1
2
3
4
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03 0.04
2 eV -5/102mδ6.5 7.0 7.5 8.0 8.50
1
2
3
4
2 eV -3/102m∆2.0 2.2 2.4 2.6 2.8
π/δ0.0 0.5 1.0 1.5 2.0
LBL Acc + Solar + KL + SBL Reactors
σNσN
NHIH
δCP
sin δ ~ -1 (or sin δ < 0)
favored; sin δ ~ +1 excluded
6.5 7 7.5 8 8.50
1
2
3
4
2 2.2 2.4 2.6 2.80
1
2
3
4
0 0.5 1 1.5 20
1
2
3
4
0.25 0.3 0.350
1
2
3
4
0.01 0.015 0.02 0.025 0.030
1
2
3
4
0.3 0.4 0.5 0.6 0.70
1
2
3
4
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND + SBL Reactors
NHIH
6.5 7 7.5 8 8.50
1
2
3
4
2 2.2 2.4 2.6 2.80
1
2
3
4
0 0.5 1 1.5 20
1
2
3
4
0.25 0.3 0.350
1
2
3
4
0.01 0.015 0.02 0.025 0.030
1
2
3
4
0.3 0.4 0.5 0.6 0.70
1
2
3
4
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND + SBL Reactors + Atmos
NOIO
6.5 7 7.5 8 8.50
1
2
3
4
2 2.2 2.4 2.6 2.80
1
2
3
4
0 0.5 1 1.5 20
1
2
3
4
0.25 0.3 0.350
1
2
3
4
0.01 0.015 0.02 0.025 0.030
1
2
3
4
0.3 0.4 0.5 0.6 0.70
1
2
3
4
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND + SBL Reactors + Atmos
NOIO
6.5 7 7.5 8 8.50
1
2
3
4
2 2.2 2.4 2.6 2.80
1
2
3
4
0 0.5 1 1.5 20
1
2
3
4
0.25 0.3 0.350
1
2
3
4
0.01 0.015 0.02 0.025 0.030
1
2
3
4
0.3 0.4 0.5 0.6 0.70
1
2
3
4
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND + SBL Reactors + Atmos
NOIO
More on unknown oscillation parameters: 12
6.5 7 7.5 8 8.50
1
2
3
4
2 2.2 2.4 2.6 2.80
1
2
3
4
0 0.5 1 1.5 20
1
2
3
4
0.25 0.3 0.350
1
2
3
4
0.01 0.015 0.02 0.025 0.030
1
2
3
4
0.3 0.4 0.5 0.6 0.70
1
2
3
4
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.015 0.02 0.025 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND
NHIH
6.5 7 7.5 8 8.50
1
2
3
4
2 2.2 2.4 2.6 2.80
1
2
3
4
0 0.5 1 1.5 20
1
2
3
4
0.25 0.3 0.350
1
2
3
4
0.01 0.015 0.02 0.025 0.030
1
2
3
4
0.3 0.4 0.5 0.6 0.70
1
2
3
4
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND + SBL Reactors
NHIH
6.5 7 7.5 8 8.50
1
2
3
4
2 2.2 2.4 2.6 2.80
1
2
3
4
0 0.5 1 1.5 20
1
2
3
4
0.25 0.3 0.350
1
2
3
4
0.01 0.015 0.02 0.025 0.030
1
2
3
4
0.3 0.4 0.5 0.6 0.70
1
2
3
4
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.015 0.02 0.025 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND
NHIH
LBL+Sol+KL +SBL Reac +Atmos
θ23
Δχ2 (IO-NO)
octant
+1.1 +1.1 +3.6
12θ2sin0.25 0.30 0.35
0
1
2
3
4
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03 0.04
2 eV -5/102mδ6.5 7.0 7.5 8.0 8.50
1
2
3
4
2 eV -3/102m∆2.0 2.2 2.4 2.6 2.8
π/δ0.0 0.5 1.0 1.5 2.0
LBL Acc + Solar + KL + SBL Reactors
σNσN
NHIH
Compare the current results (circa 2017) with...
6.5 7 7.5 8 8.50
1
2
3
4
2 2.2 2.4 2.6 2.80
1
2
3
4
0 0.5 1 1.5 20
1
2
3
4
0.25 0.3 0.350
1
2
3
4
0.01 0.015 0.02 0.025 0.030
1
2
3
4
0.3 0.4 0.5 0.6 0.70
1
2
3
4
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND + SBL Reactors + Atmos
NOIO
12θ2sin0.25 0.30 0.35
0
1
2
3
4
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03 0.04
2 eV -5/102mδ6.5 7.0 7.5 8.0 8.50
1
2
3
4
2 eV -3/102m∆2.0 2.2 2.4 2.6 2.8
π/δ0.0 0.5 1.0 1.5 2.0
LBL Acc + Solar + KL + SBL Reactors
σNσN
NHIH
δCP
6.5 7 7.5 8 8.50
1
2
3
4
2 2.2 2.4 2.6 2.80
1
2
3
4
0 0.5 1 1.5 20
1
2
3
4
0.25 0.3 0.350
1
2
3
4
0.01 0.015 0.02 0.025 0.030
1
2
3
4
0.3 0.4 0.5 0.6 0.70
1
2
3
4
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND + SBL Reactors
NHIH
6.5 7 7.5 8 8.50
1
2
3
4
2 2.2 2.4 2.6 2.80
1
2
3
4
0 0.5 1 1.5 20
1
2
3
4
0.25 0.3 0.350
1
2
3
4
0.01 0.015 0.02 0.025 0.030
1
2
3
4
0.3 0.4 0.5 0.6 0.70
1
2
3
4
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND + SBL Reactors + Atmos
NOIO
6.5 7 7.5 8 8.50
1
2
3
4
2 2.2 2.4 2.6 2.80
1
2
3
4
0 0.5 1 1.5 20
1
2
3
4
0.25 0.3 0.350
1
2
3
4
0.01 0.015 0.02 0.025 0.030
1
2
3
4
0.3 0.4 0.5 0.6 0.70
1
2
3
4
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND + SBL Reactors + Atmos
NOIO
6.5 7 7.5 8 8.50
1
2
3
4
2 2.2 2.4 2.6 2.80
1
2
3
4
0 0.5 1 1.5 20
1
2
3
4
0.25 0.3 0.350
1
2
3
4
0.01 0.015 0.02 0.025 0.030
1
2
3
4
0.3 0.4 0.5 0.6 0.70
1
2
3
4
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND + SBL Reactors + Atmos
NOIO
13
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03 0.04
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND
NHIH
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND + SBL Reactors + Atmos
NHIH
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND + SBL Reactors
NHIH
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03 0.04
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND
NHIH
LBL+Sol+KL +SBL Reac +Atmos
θ23
Δχ2 (IO-NO)
octant
-1.2 -0.9 +1.0
12θ2sin0.25 0.30 0.35
0
1
2
3
4
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03 0.04
2 eV -5/102mδ6.5 7.0 7.5 8.0 8.50
1
2
3
4
2 eV -3/102m∆2.0 2.2 2.4 2.6 2.8
π/δ0.0 0.5 1.0 1.5 2.0
LBL Acc + Solar + KL + SBL Reactors
σNσN
NHIH
12θ2sin0.25 0.30 0.35
0
1
2
3
4
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03 0.04
2 eV -5/102mδ6.5 7.0 7.5 8.0 8.50
1
2
3
4
2 eV -3/102m∆2.0 2.2 2.4 2.6 2.8
π/δ0.0 0.5 1.0 1.5 2.0
LBL Acc + Solar + KL + SBL Reactors
σNσN
NHIH
δCP
6.5 7 7.5 8 8.50
1
2
3
4
2 2.2 2.4 2.6 2.80
1
2
3
4
0 0.5 1 1.5 20
1
2
3
4
0.25 0.3 0.350
1
2
3
4
0.01 0.015 0.02 0.025 0.030
1
2
3
4
0.3 0.4 0.5 0.6 0.70
1
2
3
4
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND + SBL Reactors + Atmos
NOIO
6.5 7 7.5 8 8.50
1
2
3
4
2 2.2 2.4 2.6 2.80
1
2
3
4
0 0.5 1 1.5 20
1
2
3
4
0.25 0.3 0.350
1
2
3
4
0.01 0.015 0.02 0.025 0.030
1
2
3
4
0.3 0.4 0.5 0.6 0.70
1
2
3
4
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND + SBL Reactors + Atmos
NOIO
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND + SBL Reactors
NHIH
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND + SBL Reactors + Atmos
NHIH
6.5 7 7.5 8 8.50
1
2
3
4
2 2.2 2.4 2.6 2.80
1
2
3
4
0 0.5 1 1.5 20
1
2
3
4
0.25 0.3 0.350
1
2
3
4
0.01 0.015 0.02 0.025 0.030
1
2
3
4
0.3 0.4 0.5 0.6 0.70
1
2
3
4
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND + SBL Reactors + Atmos
NOIO
... 1yr ago, 2016: trends were somewhat weaker 14
6.5 7 7.5 8 8.50
1
2
3
4
2 2.2 2.4 2.6 2.80
1
2
3
4
0 0.5 1 1.5 20
1
2
3
4
0.25 0.3 0.350
1
2
3
4
0.01 0.015 0.02 0.025 0.030
1
2
3
4
0.3 0.4 0.5 0.6 0.70
1
2
3
4
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.015 0.02 0.025 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND
NHIH
6.5 7 7.5 8 8.50
1
2
3
4
2 2.2 2.4 2.6 2.80
1
2
3
4
0 0.5 1 1.5 20
1
2
3
4
0.25 0.3 0.350
1
2
3
4
0.01 0.015 0.02 0.025 0.030
1
2
3
4
0.3 0.4 0.5 0.6 0.70
1
2
3
4
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND + SBL Reactors
NHIH
6.5 7 7.5 8 8.50
1
2
3
4
2 2.2 2.4 2.6 2.80
1
2
3
4
0 0.5 1 1.5 20
1
2
3
4
0.25 0.3 0.350
1
2
3
4
0.01 0.015 0.02 0.025 0.030
1
2
3
4
0.3 0.4 0.5 0.6 0.70
1
2
3
4
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.015 0.02 0.025 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND
NHIH
LBL+Sol+KL +SBL Reac +Atmos
θ23
Δχ2 (IO-NO)
octant
+1.1 +1.1 +3.6
12θ2sin0.25 0.30 0.35
0
1
2
3
4
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03 0.04
2 eV -5/102mδ6.5 7.0 7.5 8.0 8.50
1
2
3
4
2 eV -3/102m∆2.0 2.2 2.4 2.6 2.8
π/δ0.0 0.5 1.0 1.5 2.0
LBL Acc + Solar + KL + SBL Reactors
σNσN
NHIH
Currently: ~2σ hints in favor of Dirac CPV, NO, and non-maximal θ23 (*)
6.5 7 7.5 8 8.50
1
2
3
4
2 2.2 2.4 2.6 2.80
1
2
3
4
0 0.5 1 1.5 20
1
2
3
4
0.25 0.3 0.350
1
2
3
4
0.01 0.015 0.02 0.025 0.030
1
2
3
4
0.3 0.4 0.5 0.6 0.70
1
2
3
4
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND + SBL Reactors + Atmos
NOIO
12θ2sin0.25 0.30 0.35
0
1
2
3
4
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03 0.04
2 eV -5/102mδ6.5 7.0 7.5 8.0 8.50
1
2
3
4
2 eV -3/102m∆2.0 2.2 2.4 2.6 2.8
π/δ0.0 0.5 1.0 1.5 2.0
LBL Acc + Solar + KL + SBL Reactors
σNσN
NHIH
δCP
6.5 7 7.5 8 8.50
1
2
3
4
2 2.2 2.4 2.6 2.80
1
2
3
4
0 0.5 1 1.5 20
1
2
3
4
0.25 0.3 0.350
1
2
3
4
0.01 0.015 0.02 0.025 0.030
1
2
3
4
0.3 0.4 0.5 0.6 0.70
1
2
3
4
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND + SBL Reactors
NHIH
6.5 7 7.5 8 8.50
1
2
3
4
2 2.2 2.4 2.6 2.80
1
2
3
4
0 0.5 1 1.5 20
1
2
3
4
0.25 0.3 0.350
1
2
3
4
0.01 0.015 0.02 0.025 0.030
1
2
3
4
0.3 0.4 0.5 0.6 0.70
1
2
3
4
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND + SBL Reactors + Atmos
NOIO
6.5 7 7.5 8 8.50
1
2
3
4
2 2.2 2.4 2.6 2.80
1
2
3
4
0 0.5 1 1.5 20
1
2
3
4
0.25 0.3 0.350
1
2
3
4
0.01 0.015 0.02 0.025 0.030
1
2
3
4
0.3 0.4 0.5 0.6 0.70
1
2
3
4
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND + SBL Reactors + Atmos
NOIO
6.5 7 7.5 8 8.50
1
2
3
4
2 2.2 2.4 2.6 2.80
1
2
3
4
0 0.5 1 1.5 20
1
2
3
4
0.25 0.3 0.350
1
2
3
4
0.01 0.015 0.02 0.025 0.030
1
2
3
4
0.3 0.4 0.5 0.6 0.70
1
2
3
4
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND + SBL Reactors + Atmos
NOIO
(*) Latest T2K data (Aug. 2017) not yet included in this fit. Update (2018) of the global analysis with these and other data is in progress
Timewilltellifthesehintswillgrowup!
15
θ23 octant + (non)max
Very personal and subjective rating of such ~2σ hints:
δCP
Δχ2 (IO-NO)
***
**
*
νe/νeappearanceprobab.seemtodifferbyCPV:Veryinteres7ng![Akintoθ13hintsbefore2012]
__
Mass-orderinginforma7onrather“diluted”indata:S7llvague,butstartstobeinteres7ng
Fragile-differentexperimentsnotyetconverging:Degeneracymightstaywithusforquitesome7me...
Hints are “entangled” as subleading effects in νeappearance channel
[They might also be entangled with BSM neutrino physics, if any]
16
0.00 0.010.02 0.030.04 0.050.06 0.070.08 0.09 0.100.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.01 0.02 0.03 0.04 0.05 0.060.0
0.5
1.0
1.5
2.0
0.00 0.010.02 0.030.04 0.050.06 0.07 0.080.09 0.100.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.01 0.02 0.03 0.04 0.05 0.060.0
0.5
1.0
1.5
2.0
0.00 0.010.020.03 0.040.05 0.060.07 0.08 0.090.100.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.01 0.02 0.03 0.04 0.05 0.060.0
0.5
1.0
1.5
2.00.00 0.010.020.03 0.040.05 0.06 0.070.08 0.090.100.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.01 0.02 0.03 0.04 0.05 0.060.0
0.5
1.0
1.5
2.0
0.00 0.010.02 0.030.04 0.050.06 0.07 0.080.09 0.100.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.01 0.02 0.03 0.04 0.05 0.060.0
0.5
1.0
1.5
2.0
0.00 0.010.020.03 0.040.05 0.060.07 0.08 0.090.100.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.01 0.02 0.03 0.04 0.05 0.060.0
0.5
1.0
1.5
2.0LBL Acc + Solar + KL + SBL Reactors + Atmos
13θ2sin 13θ2sin 13θ2sin
13θ2sin 13θ2sin 13θ2sin
π/δπ/δ
σ1σ2σ3
Norm
al Hierarchy
Inverted Hierarchy
[SupplementarytoarXiv:1703.04471]
NO
IO
2overlappingbandsfortwooctants
E.g.:(θ13,δ)covariances
θ13fromreactors(vsaccel.) Impactofatmosphericν
Hintsmay(not)convergebe\erinonemassorderingwrttheother
17
Mass ordering via oscillations
Oscillation experiments can determine the sign of ±Δm2 ...
δm2
δm2
+Δm2 -Δm2
...if they can observe interference of oscill. driven by ±Δm2 with oscill. driven by a quantity Q having known sign. Three options:
Q ~ δm2 medium-baseline reactors (a)
Q ~ GF E Ne matter effects in accel./atmosph. ν (b)
Q ~ GF E Nν self-interaction effects in supernovae (c)
(IO) (NO)
(a)JUNO(b)Atmos:KM3NeT-ORCA,PINGU,HyperK...;Accel.:DUNE,T2HK,...(c)AlloperaFnglow-Edetectors
18
Oscillation experiments can determine the sign of ±Δm2 ...
δm2
δm2
+Δm2 -Δm2
...if they can observe interference of oscill. driven by ±Δm2 with oscill. driven by a quantity Q having known sign. Three options:
(IO) (NO)
Nonoscillation searches may provide further probes of ordering à [independently on δCP and on θ23]
Q ~ δm2 medium-baseline reactors
Q ~ GF E Ne matter effects in accel./atmosph. ν
Q ~ GF E Nν self-interaction effects in supernovae
Mass ordering via oscillations 19
(mβ,mββ,Σ)
βdecay,sensiFvetothe“effecFveelectronneutrinomass”:
0νββdecay:onlyifMajorana.“EffecFveMajoranamass”:
Cosmology:DominantlysensiFvetosumofneutrinomasses:
Note 1: These observables may provide handles to distinguish NO/IO. Note 2: Majorana case gives a new source of CPV (unconstrained) Note 2: The three observables are correlated by oscillation dataà
3ν paradigm: absolute ν masses and observables 20
-1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4-4.0
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
-110 1-310
-210
-110
1
-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0-4.0
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
10
20
30
40
50
60
70
80
90
100
-310 -210 -110 1-310
-210
-110
1-1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4
-2.0
-1.5
-1.0
-0.5
0.0
-110 1-310
-210
-110
1
(NH)σ2 (IH)σ2
(eV)Σ (eV)βm
(eV)
ββm
(eV)
βm
Constraints on nonoscillation observables from oscillation data
mββspread due to
Majorana CP phase(s):
accessible in principle [but: large errors on Nuclear Matrix Elements from nuclear modeling]
NOIO
~degenerate for relatively large neutrino masses
21
-1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4-4.0
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
-110 1-310
-210
-110
1
-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0-4.0
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
10
20
30
40
50
60
70
80
90
100
-310 -210 -110 1-310
-210
-110
1-1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4
-2.0
-1.5
-1.0
-0.5
0.0
-110 1-310
-210
-110
1
(NH)σ2 (IH)σ2
(eV)Σ (eV)βm
(eV)
ββm
(eV)
βm
β :Mainz+Troitsk
Σ : CMB+LSS 0νββ :KL-Zen, GERDA, EXO, Cuore...
Upper limits on mβ,mββ,Σ(up to some syst.) + osc. constraints
Cosmological data generally prefer the smallest values for the total neutrino mass, and already contribute to put IO “under pressure” à
NOIO
22
Δχ2 (IO-NO)
+1.1 +1.1 +3.6
LBL+Sol+KL +SBL Reac +Atmos +DBD, Cosmo
+3.6 ... +4.4
Smallbutcoherentsteps:N.O.favored...Overallpreferenceat1.9σ - 2.1σ
GrandtotalofIO-NOdifferences:
Thesta^s^calsignificanceofpossiblehintsaboutorderingiscurrentlydebated.
Iftheyarenotfluctua^ons,expect(frac^onal)improvementsinupcomingyears
Dedicatedprojectsareplannedwithreactor,atmospheric,accel.neutrinos...
[See1703.04471fordetaileddiscussion]
23
-1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4-4.0
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
-110 1-310
-210
-110
1
-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0-4.0
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
10
20
30
40
50
60
70
80
90
100
-310 -210 -110 1-310
-210
-110
1-1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4
-2.0
-1.5
-1.0
-0.5
0.0
-110 1-310
-210
-110
1
(NH)σ2 (IH)σ2
(eV)Σ (eV)βm
(eV)
ββm
(eV)
βm
β :KATRIN
Σ : Precision Cosmology 0νββ :Upgraded/New expt. (+ NME)
... and on absolute masses. Upper limits on mβ,mββ,Σ in ~10 years ?
Large phase space for discoveries about ν mass and nature. Theoretical challenges: cosmo high accuracy calculations/simulations, NME uncertainties
NOIO
24
25
Once upon a time... all neutrino observations were limited by stat’s, and systematics could be treated as numbers (normalization, bias ...) Now we have as many as O(106) events collected in SBL reactors, and we expect O(105) events in each of JUNO, ORCA, PINGU etc. Systematic errors are no longer “numbers” but become “functions”. Dedicated approaches are needed to deal with such uncertainties. [This transition has already taken place in other fields, such as in parton distribution function fits and precision cosmology forecasts.] Unprecedented challenges are awaiting us in neutrino data analyses: We must be prepared to deal with “functions” which ideally should be known in size, shape, correlations and probability distributions, but in practice may also be partly (if not completely!) unknown.
Oscilla^ons:Aglimpseofupcomingchallenges...
Hard lesson learned from current reactor experiments: An unknown systematic error source (function) δΦ(E), well beyond supposedly-known shape uncertainties!
Now we know its shape, and can correct for it, but residuals do remain: energy-scale uncertainties E à E’(E) (x-axis “stretch”) flux-shape uncertainties Φ (E) à Φ’(E) (y-axis “stretch”)
From S. Jetter (TAU 2014) & J. Cao (TAUP 2015)
Daya Bay data Huber + Mueller uncert.
Daya Bay RENO Double Chooz
26
default
halved
2 3 4 5 6 7 8 90.98
0.99
1.00
1.01
1.02
2 3 4 5 6 7 8 90.8
0.9
1.0
1.1
1.2E (MeV)
E’/E
E (MeV)
Φ’/Φ
Relative 1σ error bands
Recent evaluations of energy-scale and flux-shape errors (reactors)
Dwyer & Langford 2014
B-Z. Hu @ Moriond 2015
E’(E) and Φ’(E) models
Smoothed errors assumed to be linear and symmetric (gaussian)
[Note sawtooth-like spectrum]
27
2 3 4 5 6 7 8 90.8
0.9
1.0
1.1
1.2
2 3 4 5 6 7 8 90.8
0.9
1.0
1.1
1.2
2 3 4 5 6 7 8 90.8
0.9
1.0
1.1
1.2
2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 90.98
0.99
1.00
1.01
1.02
0.98
0.99
1.00
1.01
1.02
0.98
0.99
1.00
1.01
1.02NH true
E’/E
Φ’/Φ
E (MeV) E (MeV) E (MeV)
osc. + norm. + energy scale + flux shape
0
1
2
3
4
5
0 5 10
NH trueosc. + norm.
+ energy scale+ flux shape
σN
T (y)
Energy-scale and flux-shape errors with constrained “size” but unconstrained “shape” can noticeably lower JUNO sensitivity
(Note abscissa prop. to √T)
In addition: sawtooth-like fluctuations may further affect and challenge JUNO performances! Near detector needed? [See next reactor talks]
[SeearXiv:1508.01392]
28
29
Anotherexample:effectofshapeuncertain^esonenergy-anglespectrainORCA
Time (years)
σN
0
5
10
exponential axis
0 5 10
exponential axis
Time (years)
σN
0
5
10
exponential axis
0 5 10
exponential axis
Time (years)
σN
0
5
10
exponential axis
0 5 10
exponential axis
Time (years)
σN
0
5
10
exponential axis
0 5 10
exponential axis
Time (years)
σN
0
5
10
exponential axis
0 5 10
exponential axis
Time (years)
σN
0
5
10
exponential axis
0 5 10
exponential axis
Time (years)
σN
0
5
10
exponential axis
0 5 10
exponential axis
Time (years)
σN
0
5
10
exponential axis
0 5 10
exponential axis
Stat + syst (osc+norm) + resolution (scale,width) + polynomial + uncorrelated
σN
σN
Norm
al orderingInverted ordering
Time (y) Time (y) Time (y) Time (y)
OtherfuncFonaluncertainFesinfutureexpts:differenFalneutrinocross-secFons,nuclearformfactors(includingMA,gA),inhomogeneiFesoflarge-volumedetectors,...
SeearXiv:1708.03022
“Everything we see hides another thing, we always want to see what is hidden by what we see.”
Epilogue
RenéMagri+e:
Starttohavesomehintsonνmassordering.But:unprecedented
challengesbeforewecanreally“see”it!Surprises?
Extra slides
Currentindica^onΔχ2ΙΟ-ΝΟ= 3.6 fromoscill.datastartstobeinteres^ng.
Usefultoseetheeffectofexcluding/includingthisoffsetintheanalysis:
6.5 7 7.5 8 8.50
1
2
3
4
2 2.2 2.4 2.6 2.80
1
2
3
4
0 0.5 1 1.5 20
1
2
3
4
0.25 0.3 0.350
1
2
3
4
0.01 0.015 0.02 0.025 0.030
1
2
3
4
0.3 0.4 0.5 0.6 0.70
1
2
3
4
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2 2.2 2.4 2.6 2.8
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
13θ2sin0.01 0.02 0.03
σN
0
1
2
3
4
σN
0
1
2
3
4
LBL Acc + Solar + KamLAND + SBL Reactors + Atmos
NOIO
6.5 7 7.5 8 8.50
5
10
15
2.4 2.5 2.6 2.70
5
10
15
0 0.5 1 1.5 20
5
10
15
0.25 0.3 0.350
5
10
15
1.8 2 2.2 2.4 2.60
5
10
15
0.3 0.4 0.5 0.6 0.70
5
10
15
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2.4 2.5 2.6 2.7
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
-2/1013θ2sin1.8 2 2.2 2.4 2.6
0
5
10
15
0
5
10
15
2χ
2χ
Oscillation parameters
NOI O
Twodifferentwaysofmarginalizingovermassordering(s)à
parameterP
Applya“Δχ2cut”toSEPARATEminimainNO,IO....
χ2
(doesnotincludeIO-NOoffsetinformaFon)
parameterP
...orminimizeandexpandoverANYORDERING
χ2
(includesIO-NOoffsetinformaFon)
offset
6.5 7 7.5 8 8.50
5
10
15
2.4 2.5 2.6 2.70
5
10
15
0 0.5 1 1.5 20
5
10
15
0.25 0.3 0.350
5
10
15
1.8 2 2.2 2.4 2.60
5
10
15
0.3 0.4 0.5 0.6 0.70
5
10
15
2 eV-5/102mδ6.5 7 7.5 8 8.5
2 eV-3/102m∆2.4 2.5 2.6 2.7
π/δ0 0.5 1 1.5 2
12θ2sin0.25 0.3 0.35
23θ2sin0.3 0.4 0.5 0.6 0.7
-2/1013θ2sin1.8 2 2.2 2.4 2.6
0
5
10
15
0
5
10
15
2χ
2χ
Oscillation parameters
NOI O
Oscilla^onparameterranges
1.4− 1.2− 1.0− 0.8− 0.6− 0.4− 0.2− 0.0−3.0−
2.5−
2.0−
1.5−
1.0−
0.5−
0.0
10
20
30
40
50
60
70
80
90
100
23θ 2sin
1−10 1
13θ 2si
n
3−10
2−10
1−10
1
23θ 2sin
1−10 1
13θ 2si
n
3−10
2−10
1−10
1Oscillations
SeparateNO IO,
)σ and 3σ(2
AnyOrdering
(eV)Σ (eV)Σ
(eV)
ββm
Sumofneutrinomasses(Cosmology)
EffecFveMajoranaMass(DB
D)
Absoluteneutrinomassobservables
spreadfromMajoranaCPVphases
0νββ Cosmo
yr)25 (101/2T
0 5 10 15 20 25 30 35 40
2 χ∆
0
1
2
3
4
5
6
7
8
9
10KamLAND-Zen Phase-I
KamLAND-Zen Phase-II
KamLAND-Zen Combined
EXO-200 (2014)
KamLAND-Zenhalf-lifelimits
+NMELikelihoodbasedon:E.L.,A.Rotunno,F.Simkovic,arXiv:1506.04058
Currentleading0νββconstraints
2−10 1−100
1
2
3
4
5
6
7
8
9
10
(eV)ββm
2χ
(KamLAND-Zen)ββν0
sub-eV
1.4− 1.2− 1.0− 0.8− 0.6− 0.4− 0.2− 0.0−3.0−
2.5−
2.0−
1.5−
1.0−
0.5−
0.0
20
40
60
80
100
120
140
160
180
23θ 2sin
1−10 1
13θ 2si
n
3−10
2−10
1−10
1
23θ 2sin
1−10 1
13θ 2si
n
3−10
2−10
1−10
1ββνOscill. + 0
SeparateNO IO,
AnyOrdering
(eV)Σ (eV)Σ
(eV)
ββm
Analysisofvariousdatasetswithinstandard(6-param.)ΛCDMmodelaugmentedwithΣplusonepossible1extraparameterAlens,toaccountforsyst’sornonstandardeffects[Alens>1maybetypicallytradedforhighervaluesofthesumofneutrinomassΣ]
Code:CosmoMCwithNO/IOop^onsexplicitlyincludedinΣ, viathetwomass2differences
àunphysicalspectraofneutrinomasses(e.g.,Σ =0)notallowedbyconstrucFon.àexpectsmallNO-IOdifferencesatlowΣ,butvanishingathighΣ(degeneratespectrum)
Cosmologicalconstraints(circa2017)
Cosmologicalconstraints(circa2017)
Analysisofvariousdatasetswithinstandard(6-param.)ΛCDMmodelaugmentedwithΣplusonepossible1extraparameterAlens,toaccountforsyst’sornonstandardeffects[Alens>1maybetypicallytradedforhighervaluesofthesumofneutrinomassΣ]
Code:CosmoMCwithNO/IOop^onsexplicitlyincludedinΣ, viathetwomass2differences
àunphysicalspectraofneutrinomasses(e.g.,Σ =0)notallowedbyconstrucFon.àexpectsmallNO-IOdifferencesatlowΣ,butvanishingathighΣ(degeneratespectrum)
ResultsonΣ (upperbounds)andonΔχ2ΙΟ-ΝΟ:
χ2profileforNO,IOinrepresenta^vecases
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
1
2
3
4
5
6
7
8
9
10
#10
#1
#9#6
Cosmology
(eV)Σ
2χ
IO
NO
convergenceofNO,IOcurvesathighΣ
bifurca^onofNO,IOcurvesatlowΣ
Thresholds:Σ>0.06eV(NO) Σ>0.10eV(IO) Σ=0:notallowed
bestfitΣ maybeabovethreshold
Grandtotal:combina^onofoscilla^on+nonoscilla^ondata(withincreasinglystrongcosmologicalconstraints)
1.4− 1.2− 1.0− 0.8− 0.6− 0.4− 0.2− 0.0−3.0−
2.5−
2.0−
1.5−
1.0−
0.5−
0.0
10
20
30
40
50
60
70
80
90
100
23θ 2sin
1−10 1
13θ 2si
n
3−10
2−10
1−10
1
23θ 2sin
1−10 1
13θ 2si
n
3−10
2−10
1−10
1Oscillations
SeparateNO IO,
)σ and 3σ(2
AnyOrdering
(eV)Σ (eV)Σ
(eV)
ββm
1.4− 1.2− 1.0− 0.8− 0.6− 0.4− 0.2− 0.0−3.0−
2.5−
2.0−
1.5−
1.0−
0.5−
0.0
20
40
60
80
100
120
140
160
180
23θ 2sin
1−10 1
13θ 2si
n
3−10
2−10
1−10
1
23θ 2sin
1−10 1
13θ 2si
n
3−10
2−10
1−10
1ββνOscill. + 0
SeparateNO IO,
AnyOrdering
(eV)Σ (eV)Σ
(eV)
ββm
1.4− 1.2− 1.0− 0.8− 0.6− 0.4− 0.2− 0.0−3.0−
2.5−
2.0−
1.5−
1.0−
0.5−
0.0
20
40
60
80
100
120
140
160
180
23θ 2sin
1−10 1
13θ 2si
n
3−10
2−10
1−10
1
23θ 2sin
1−10 1
13θ 2si
n
3−10
2−10
1−10
1 + CosmoββνOscill. + 0 #10
SeparateNO IO,
AnyOrdering
(eV)Σ (eV)Σ
(eV)
ββm
[Casewith“conservaFve”boundsfromcosmology]
1.4− 1.2− 1.0− 0.8− 0.6− 0.4− 0.2− 0.0−3.0−
2.5−
2.0−
1.5−
1.0−
0.5−
0.0
20
40
60
80
100
120
140
160
180
200
23θ 2sin
1−10 1
13θ 2si
n
3−10
2−10
1−10
1
23θ 2sin
1−10 1
13θ 2si
n
3−10
2−10
1−10
1 + CosmoββνOscill. + 0 #9
SeparateNO IO,
AnyOrdering
(eV)Σ (eV)Σ
(eV)
ββm
[RHSplot(innerredcurve)showshowacosmological“claim”ofΣ>0 couldlooklike]
1.4− 1.2− 1.0− 0.8− 0.6− 0.4− 0.2− 0.0−3.0−
2.5−
2.0−
1.5−
1.0−
0.5−
0.0
20
40
60
80
100
120
140
160
180
200
23θ 2sin
1−10 1
13θ 2si
n
3−10
2−10
1−10
1
23θ 2sin
1−10 1
13θ 2si
n
3−10
2−10
1−10
1 + CosmoββνOscill. + 0 #6
SeparateNO IO,
AnyOrdering
(eV)Σ (eV)Σ
(eV)
ββm
[Casewith“aggressive”boundsfromcosmology]
Δχ2 (IO-NO)
+1.1 +1.1 +3.6
LBL+Sol+KL +SBL Reac +Atmos +DBD, Cosmo
+3.6 ... +4.4
Smallbutcoherentsteps:N.O.favored...Overallpreferenceat1.9σ - 2.1σ
GrandtotalofIO-NOdifferences:
Thesta^s^calsignificanceofpossiblehintsaboutorderingiscurrentlydebated.Iftheyarenotfluctua^ons,expect(frac^onal)improvementsinupcomingyearsDedicatedprojectsareplannedwithreactor,atmospheric,acceleratorneutrinos
-1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4-4.0
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
-110 1-310
-210
-110
1
-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0-4.0
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
10
20
30
40
50
60
70
80
90
100
-310 -210 -110 1-310
-210
-110
1-1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4
-2.0
-1.5
-1.0
-0.5
0.0
-110 1-310
-210
-110
1
(NH)σ2 (IH)σ2
(eV)Σ (eV)βm
(eV)
ββm
(eV)
βm
With “dreamlike” and converging data one could, e.g.
Check3νconsistency…
IdenFfythehierarchy…
ProbetheMajoranaphase(s)…
Determinethemassscale…
27
-1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4-4.0
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
-110 1-310
-210
-110
1
-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0-4.0
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
10
20
30
40
50
60
70
80
90
100
-310 -210 -110 1-310
-210
-110
1-1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4
-2.0
-1.5
-1.0
-0.5
0.0
-110 1-310
-210
-110
1
(NH)σ2 (IH)σ2
(eV)Σ (eV)βm
(eV)
ββm
(eV)
βm
But alternative situations (surprises!) might also occur....
?
?
something wrong ?
new physics ?
why the mismatch ?
28
Physics beyond “3 light ν” should always be kept in mind, e.g., in neutrinoless double beta decay:
u e e u
W W ν
Standard
u e e u
W W N
Heavyν
u e e u
Kaluza-Klein
W W ν(n)
u e e u
WR,L
νL,R RHCλ,ηλ=RHhad,η=LHhad
WR,L
e u u e
u u g
SUSYg
~ ~ ~
~
p e e p
π
SUSYπ
π SUSY
29
More on known oscillation parameters: sinergyonΔm2
0.2 0.3 0.4 0.5 0.6 0.7 0.82.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
0
50
100
150
200
250
300
350
400
450
23θ2sin
0.3 0.4 0.5 0.6 0.7
2 e
V3
10
× m
^2∆
2.0
2.2
2.4
2.6
2.8
0.2 0.3 0.4 0.5 0.6 0.7 0.82.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
0
50
100
150
200
250
300
350
400
450
23θ2sin
0.3 0.4 0.5 0.6 0.7
2 e
V3
10
× m
^2∆
2.0
2.2
2.4
2.6
2.8
0.2 0.3 0.4 0.5 0.6 0.7 0.82.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
0
50
100
150
200
250
300
350
400
450
23θ2sin
0.3 0.4 0.5 0.6 0.7
2 e
V3
10
× m
^2∆
2.0
2.2
2.4
2.6
2.80.2 0.3 0.4 0.5 0.6 0.7 0.82.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
0
50
100
150
200
250
300
350
400
450
23θ2sin
0.3 0.4 0.5 0.6 0.7
2 e
V3
10
× m
^2∆
2.0
2.2
2.4
2.6
2.8
0.2 0.3 0.4 0.5 0.6 0.7 0.82.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
0
50
100
150
200
250
300
350
400
450
23θ2sin
0.3 0.4 0.5 0.6 0.7
2 e
V3
10
× m
^2∆
2.0
2.2
2.4
2.6
2.8
0.2 0.3 0.4 0.5 0.6 0.7 0.82.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
0
50
100
150
200
250
300
350
400
450
23θ2sin
0.3 0.4 0.5 0.6 0.7
2 e
V3
10
× m
^2∆
2.0
2.2
2.4
2.6
2.8LBL Acc + Solar + KL + SBL Reactors + Atmos
23θ2sin 23θ2sin 23θ2sin
23θ2sin 23θ2sin 23θ2sin
2 e
V-3
/10
2m
∆2
eV
-3/1
02
m∆
σ1σ2σ3
Norm
al Hierarchy
Inverted Hierarchy
Norm
alOrdering
InvertedOrdering
EachofthesethreedatasetscontributestoconstrainΔm2
12
0.2 0.3 0.4 0.5 0.6 0.7 0.80.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
0.3 0.4 0.5 0.6 0.70.0
0.5
1.0
1.5
2.0
0.2 0.3 0.4 0.5 0.6 0.7 0.80.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
0.3 0.4 0.5 0.6 0.70.0
0.5
1.0
1.5
2.0
0.2 0.3 0.4 0.5 0.6 0.7 0.80.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
0.3 0.4 0.5 0.6 0.70.0
0.5
1.0
1.5
2.00.2 0.3 0.4 0.5 0.6 0.7 0.80.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
0.3 0.4 0.5 0.6 0.70.0
0.5
1.0
1.5
2.0
0.2 0.3 0.4 0.5 0.6 0.7 0.80.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
0.3 0.4 0.5 0.6 0.70.0
0.5
1.0
1.5
2.0
0.2 0.3 0.4 0.5 0.6 0.7 0.80.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
0.3 0.4 0.5 0.6 0.70.0
0.5
1.0
1.5
2.0LBL Acc + Solar + KL + SBL Reactors + Atmos
23θ2sin 23θ2sin 23θ2sin
23θ2sin 23θ2sin 23θ2sin
π/δπ/δ
σ1σ2σ3
Norm
al Hierarchy
Inverted Hierarchy
SupplementarytoarXiv:1703.04471